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数值分析PDF|Epub|txt|kindle电子书版本网盘下载
- 苏岐芳主编 著
- 出版社： 北京：中国铁道出版社
- ISBN：7113079873
- 出版时间：2007
- 标注页数：310页
- 文件大小：31MB
- 文件页数：321页
- 主题词：数值计算－高等学校－教材－英、汉
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图书目录
1 Error Analysis1
1.1 Introduction1
1.2 Sources of Errors2
1.3 Errors and Significant Digits4
1.4 Error Propagation8
1.5 Qualitative Analysis and Control of Errors10
1.5.1 Ill-condition Problem and Condition Number10
1.5.2 The Stability of Algorithm10
1.5.3 The Control of Errors12
1.6 Computer Experiments15
1.6.1 Functions Needed in The Experiments by Mathematica15
1.6.2 Experiments by Mathematica15
1.6.3 Functions Needed in The Experiments by Matlab17
1.6.4 Experiments by Matlab17
2 Interpolating20
2.1 Introduction21
2.2 Basic Concepts22
2.3 Lagrange Interpolation23
2.3.1 Linear and Parabolic Interpolation23
2.3.2 Lagrange Interpolation Polynomial26
2.3.3 Interpolation Remainder and Error Estimate27
2.4 Divided-differences and Newton Interpolation31
2.5 Differences and Newton Difference Formulae35
2.5.1 Differences35
2.5.2 Newton Difference Formulae38
2.6 Hermite Interpolation41
2.7 Piecewise Low Degree Interpolation45
2.7.1 Ill-posed Properties of High Degree Interpolation45
2.7.2 Piecewise Linear Interpolation45
2.7.3 Piecewise Interpolation of Hermite with Degree Three46
2.8 Cubic Spline Interpolation48
2.8.1 Definition of Cubic Spline48
2.8.2 The Construction of Cubic Spline49
2.9 Computer Experiments52
2.9.1 Functions Needed in The Experiments by Mathematica52
2.9.2 Experiments by Mathematica53
3 Best Approximation63
3.1 Introduction63
3.2 Norms64
3.2.1 Vector Norms64
3.2.2 Matrix Norms69
3.3 Spectral Radius71
3.4 Best Linear Approximation75
3.4.1 Basic Concepts and Theories75
3.4.2 Best Linear Approximation76
3.5 Discrete Least Squares Approximation78
3.6 Least Squares Approximation and Orthogonal Polynomials83
3.7 Computer Experiments89
3.7.1 Functions Needed in The Experiments by Mathematica89
3.7.2 Experiments by Mathematica90
3.7.3 Functions Needed in The Experiments by Matlab96
3.7.4 Experiments by Matlab96
4 Numerical Integration and Differentiation99
4.1 Introduction100
4.2 Interpolatory Quadratures101
4.2.1 Interpolatory Quadratures101
4.2.2 Degree of Accuracy102
4.3 Newton-Cotes Quadrature Formula103
4.4 Composite Quadrature Formula109
4.4.1 Composite Trapezoidal Rule109
4.4.2 Composite Simpson's Rule110
4.5 Romberg Integration111
4.5.1 Recursive Trapezoidal Rule111
4.5.2 Romberg Algorithm112
4.5.3 Richardson's Extrapolation114
4.6 Gaussian Quadrature Formula115
4.7 Numerical Differentiation120
4.7.1 Numerical Differentiation120
4.7.2 Differentiation Polynomial Interpolation121
4.7.3 Richardson's Extrapolation126
4.8 Computer Experiments128
4.8.1 Functions Needed in The Experiments by Mathematica128
4.8.2 Experiments by Mathematica129
4.8.3 Experiments by Matlab134
5 Solution of Nonlinear Equations138
5.1 Introduction138
5.2 Basic Theories141
5.3 Bisection Method142
5.4 Iterative Method and Its Convergence144
5.4.1 Fixed Point and Iteration144
5.4.2 Global Convergence145
5.4.3 Local Convergence148
5.4.4 Order ofConvergence150
5.5 Accelerating Convergence151
5.6 Newton's Method153
5.6.1 Newton's Method and Its Convergence153
5.6.2 Reduced Newton Method and Newton's Descent Method155
5.6.3 The Case of Multiple Roots156
5.7 Secant Method and Muller Method158
5.7.1 Secant Method158
5.7.2 Muller Method159
5.8 Systems of Nonlinear Equations160
5.9 Computer Experiments163
5.9.1 Functions Needed in The Experiments by Mathematica163
5.9.2 Experiments by Mathematica163
5.9.3 Experiments by Matlab168
6 Direct Methods for Solving Linear Systems172
6.1 Introduction173
6.2 Gaussian Elimination174
6.2.1 Basic Gaussian Elimination174
6.2.2 Triangular Decomposition178
6.3 Gaussian Elimination with Column Pivoting181
6.4 Methods of The Triangular Decomposition183
6.4.1 The Direct Methods of The Triangular Decomposition183
6.4.2 The Square Root Method185
6.4.3 The Speedup Method188
6.5 Analysis of Round-off Errors191
6.5.1 Condition Number191
6.5.2 Iterative Refinement195
6.6 Computer Experiments197
6.6.1 Functions Needed in The Experiments by Mathematica197
6.6.2 Experiments by Mathematica197
6.6.3 Functions Needed in The Experiments by Matlab203
6.6.4 Experiments by Matlab203
7 Iterative Techniques for Solving Linear Systems209
7.1 Introduction210
7.2 Basic Iterative Methods212
7.2.1 Jacobi Method213
7.2.2 Gauss-Seidel Method215
7.2.3 SOR Method216
7.3 Iterative Method Convergence217
7.3.1 Basic Theorems217
7.3.2 Some Special Systems of Equations222
7.4 Computer Experiments226
7.4.1 Functions Needed in The Experiments by Mathematica226
7.4.2 Experiments by Mathematica227
8 Numerical Solution of Ordinary Differential Equations234
8.1 Introduction234
8.2 The Existence and Uniqueness of Solutions236
8.3 Taylor-Series Method238
8.4 Euler's Method240
8.5 Single-step Methods243
8.5.1 Single-step Methods243
8.5.2 Local Truncation Error244
8.6 Runge-Kutta Methods245
8.6.1 Second-Order Runge-Kutta Method245
8.6.2 Fourth-Order Runge-Kutta Method246
8.7 Multistep Methods248
8.7.1 General Formulas of Multistep Methods248
8.7.2 Adams Explicit and Implicit Formulas249
8.8 Systems and Higher-Order Differential Equations252
8.8.1 Vector Notation253
8.8.2 Taylor-Series Method for Systems255
8.8.3 Fourth-Order Runge-Kutta Formula for Systems256
8.9 Computer Experiments258
8.9.1 Functions Needed in The Experiments by Mathematica258
8.9.2 Experiments by Mathematica258
附录266
附录A Mathematica基本操作266
附录B Matlab基本操作285
附录C Answers to Selected Problems305
参考文献310